The transition from centralized control to distributed decision-making has been one of the most important engineering developments to occur in recent decades. In many complex systems, de-centralizing the system's behavior improves flexibility and robustness while simultaneously decreasing the size and cost of the individual devices. In order for a set of distributed devices to coordinate, most distributed systems require a means of synchronizing operations across devices. Many such systems assume the availability of a single signal which is available to all of the distributed devices. Obtaining such a synchronized signal in a distributed system is a long-standing engineering challenge. Traditional approaches have either required some measure of centralized recalibration over the local oscillators that time operations at each individual device, or assume the perfect synchrony of such oscillators as a matter of design. The former approach fails to achieve true de-centralization, and the latter approach is unachievable in practice.
Beamforming, the creation of a coherent beam at a target location by the calculated interference of beams generated by a set of distributed devices, has important applications in communications, geolocation and defense systems. Traditional beamforming systems follow either a standard or a retrodirective paradigm. Traditional standard beamforming techniques are able to create a coherent beam at an arbitrary target location, but require precise knowledge of the position of each of the individual devices. Traditional retrodirective beamforming techniques do not require any knowledge of the positions of the individual devices, but require a single beacon emitting a periodic signal at a fixed frequency and are limited to creating a coherent beam with that same fixed frequency at the location of the beacon. These techniques have failed to achieve the important goals of repositioning the coherent beam at a location different from the beacon location, or at a frequency different from the beacon frequency, without precise knowledge of the device positions. The deficiencies in traditional approaches to distributed synchronization and beamforming are addressed by the invention described herein.